Global well-posedness for the fifth order Kadomtsev–Petviashvili II equation in three dimensional space. (January 2016)

• Record Type: Journal Article
• Authors: Li, Junfeng; Meng, Kun
• Is Part Of: Nonlinear analysis. Volume 130(2015)
• Page Start: 157
• Page End: 175
• Publication Date: 2016-01
• Subjects: 35Q53, 35Q55; Fifth order Kadomtsev–Petviashvili II equation -- Well-posedness -- Scattering -- Critical space -- Bilinear estimate -- Up and Vp spaces; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.09.030
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The Cauchy problem for the fifth order Kadomtsev–Petviashvili II equation ∂ x ( ∂ t u − ∂ x 5 u + ∂ x ( u 2 ) ) + △ y z u = 0 is considered. A small data global well-posedness and scattering result in the scale and Galilean invariant space H ̇ − 1 2, 0, 0 ( R 3 ) is derived.